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drummers-lowrise
11) Message boards : General discussion : Implementing an Algorithm? (Message 153018)
Posted 228 days ago by Profile BurProject donor
You can write a simple Pari GP program:
for (k=1, oo, n=3^k+2; if (Mod(2, n)^((n-1)/2) == -1, print(k); if (!ispseudoprime(n), print("Failed!"))));

The test checks if n is an Euler–Jacobi pseudoprime.
So this first checks whether n is prime under the assumption that the conjecture is true and then, additionally, does a PRP test as a means to potentially disprove the conjecture?

Because 3^k + 2 increases exponentially, if n is a PRP then it is most likely prime.
Why is that? Couldn't any number be written as 3^k + m and thus increase exponentially with increasing k?

Is the test for primality under the assumption of the conjecture to be true computationally faster than a PRP test? If so, it could be an interesting way to generate large PRPs.
12) Message boards : Generalized Fermat Prime Search : Guess the number of digits in the LAST GFN-17-LOW prime (Message 152968)
Posted 229 days ago by Profile BurProject donor
999,909 digits.

Should correspond to a base between 42518334 and 42519078. If my PARI game isn't way off.
13) Message boards : Number crunching : Sabotage of Number Crunching (Message 152964)
Posted 229 days ago by Profile BurProject donor
And Mr Wunk never noticed he had zero successful WUs? Or at least that his score didn't increase?

Nice to know it's finally solved... :D
14) Message boards : General discussion : Get prime from concatenating first n numbers (Message 152778)
Posted 238 days ago by Profile BurProject donor
Ah, I had read ?logint but didn't see why it could be used at first.

So the output of logint(a,b) is always identical to floor(log_b(a)) it just saves computing time by not going through the actual calculation of the log?

Interesting take on the & instead of if. Now I realized I actually used that a couple of times before just not in such simple constructs but only within an if clause to indicate progress by throwing an &!(print(...)) in there. Btw, is it convention that print(a) returns 0 upon successfully printing?
15) Message boards : Extended Sierpinski Problem : k = 202705 (Message 152776)
Posted 238 days ago by Profile BurProject donor
If I'm not wrong and also assuming a sieving percentage of 1%, about 23000 tests are required to produce a mega prime.

1% sounds a bit optimistic to me. My rule of thumb is that the number of tasks needed to find a prime is roughly #(digits)/30.
That would correspond to a sieving rate of about 1.4%?

Btw, I was looking at the stats and saw that the number of workunits per 1M range of k for Woodall numbers decreases steadily with increasing k. For example 1M < k < 2M there were 36000 workunits and for 18M < k < 19M there were only 28000. Cullen shows a similar trend, but way less pronounced.

Were the larger numbers sieved more deeply or is there another reason?
16) Message boards : General discussion : Get prime from concatenating first n numbers (Message 152773)
Posted 239 days ago by Profile BurProject donor
Jeppe, I tried the same, but my code for creating the number is a bit more complicated... :)

m=2000;p=0;k=0;for (i=1,m,k+=ceil(log(i)/log(10));p+=i*10^k;if(ispseudoprime(p),print("Prime: ",p)))



And the other suggested format of increasing and then decreasing values like 12345678910987654321:

updown(r,s) = {
b=s;
for(a=r,s-1,
p=0;k=0;for (i=a,b,p+=i*10^k;k+=(floor(log(i)/log(10))+1));
q=0;k=0;for (i=1,b-a,j=b-i;q+=j*10^k;k+=(floor(log(j)/log(10))+1));
p+=q*10^(floor(log(p)/log(10))+1);
\\ print(p);
if(ispseudoprime(p),print("yay: ",p," is prime!"))
)
}

And to run it: for(i=2,100,updown(1,i)) tests all number with 2 ... 100 in the middle and beginning at 1 to the middle value. Such as 121, 232, 12321, 343, 23432, 1234321, ...

Your slim code could be used there as well though. I got to understand what's going on there at first though.
17) Message boards : General discussion : Suggestions for 2022 challenges (Message 152762)
Posted 240 days ago by Profile BurProject donor
I would like it a lot if Primorials/Factorials could be transferred into Boinc. No one is really investigating these numbers and thus progress is very slow. The last prime of the Primorial+1 form was discovered 20 years ago. That form is quite interesting though due to its link to the proof of the infinitude of primes.

But challenges to finally get PPS and GFN-17 low to merge into the Mega counterparts would be very nice as well.
18) Message boards : Extended Sierpinski Problem : k = 202705 (Message 152752)
Posted 241 days ago by Profile BurProject donor
Same here. It depends a lot on the projects you crunch how fast you'll succeed. Going with the conjectures obviously makes success rather unlikely, while PPS and GFN-17 Mega should provide a hit faster. If I'm not wrong and also assuming a sieving percentage of 1%, about 23000 tests are required to produce a mega prime. A somewhat decent 10-core can maybe do 400 tests a day, so it should take 2 months.

GFN-17 is a bit more complicated due to DC, so unless you have a very fast card, going by CPU is probably the better choice.
19) Message boards : Wieferich and Wall-Sun-Sun Prime Search : Ratio between near-WW primes (Message 152747)
Posted 241 days ago by Profile BurProject donor
No new near-WWSSprimes this week. Not unexpected, since during the challenge the completion rate had dropped from 14k/day to 5k/day. It's back up again though, so unless many computers take a break over the christmas holidays, hopefully this week will fare better again.

Update 20-12-2021

Tests upper bound: 9.9e18 / 18e18 (54 %, +1 %) Number of near-WW found: 308 (+-0) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 308 | - | - 100 | 34 | 31 | +10 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 15 % (+- 0%). At 18e18 we would reach: 29 % (-0 %) 100 % would be reached at: 64e18 (+0e18)
20) Message boards : Sierpinski/Riesel Base 5 Problem : Riesel k=273662 eliminated (Message 152674)
Posted 246 days ago by Profile BurProject donor
On December 7th, the 2441715 digit prime (ranked #97)

273662 * 5^3493296 - 1

was found by user Lukas, eliminating k = 273662 from the Riesel base 5 conjecture.

Already the second conjecture k removed in a short while.


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